{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"45%\" align=\"right\" border=\"4\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Single-Risk Derivatives Valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This part introduces into the modeling and valuation of derivatives instruments (contingent claims) based on a single risk factor (e.g. a stock price, stock index level or interest rate). It also shows how to model and value portfolios composed of such instruments. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dx import *\n",
    "from pylab import plt\n",
    "plt.style.use('seaborn')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following **single risk factor valuation classes** are available:\n",
    "\n",
    "* `valuation_mcs_european_single` for derivatives with European exercise\n",
    "* `valuation_mcs_american_single` for derivatives with American/Bermudan exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling the Risk Factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before moving on to the valuation classes, we need to model an instantiate an underlying risk factor, in this case a `geometric_brownian_motion` object. Background information is provided in the respective part of the documentation about model classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = constant_short_rate('r', 0.06)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "me = market_environment('me', dt.datetime(2015, 1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "me.add_constant('initial_value', 36.)\n",
    "me.add_constant('volatility', 0.2)\n",
    "me.add_constant('final_date', dt.datetime(2015, 12, 31))\n",
    "me.add_constant('currency', 'EUR')\n",
    "me.add_constant('frequency', 'W')\n",
    "me.add_constant('paths', 25000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "me.add_curve('discount_curve', r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "gbm = geometric_brownian_motion('gbm', me)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## valuation_mcs_european_single"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first instrument we value is a European call option written on the single relevant risk factor as embodied by the `gbm` model object. To this end, we add a **maturity date** to the market environment and a **strike price**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "me.add_constant('maturity', dt.datetime(2015, 12, 31))\n",
    "me.add_constant('strike', 40.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To instantiate a the `valuation_mcs_european_single` class, the following information/data is to be provided:\n",
    "\n",
    "* name as a `string` object\n",
    "* instance of a model class\n",
    "* market environment\n",
    "* payoff of the instrument a `string` object and containing \"regular\" Python/NumPy code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "call_eur = valuation_mcs_european_single(\n",
    "                name='call_eur',\n",
    "                underlying=gbm,\n",
    "                mar_env=me,\n",
    "                payoff_func='np.maximum(maturity_value - strike, 0)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, the payoff is that of a regular, plain vanilla European call option. If $T$ is the maturity date, $S_T$ the value of the relevant risk factor at that date and $K$ the strike price, the payoff $h_T$ at maturity of such an option is given by\n",
    "\n",
    "$$\n",
    "h_T = \\max[S_T - K, 0]\n",
    "$$\n",
    "\n",
    "`maturity_value` represents the value vector of the risk factor at maturity. Any other \"sensible\" payoff definition is possible. For instance, the following works as well: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "payoff = 'np.maximum(np.minimum(maturity_value) * 2 - 50, 0)'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other standardized payoff elemenets include `mean_value, max_value` and `min_value` representing maturity value vectors with the pathwise means, maxima and minima. Using these payoff elements allows the easy definition of options with **Asian features**.\n",
    "\n",
    "\n",
    "Having instantiated the valuation class, the `present_value` method returns the present value Monte Carlo estimator for the call option."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.172619"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "call_eur.present_value()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the `delta` and `vega` methods return the delta and the vega of the option, estimated numerically by a forward difference scheme and Monte Carlo simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4491"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "call_eur.delta()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.1882"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "call_eur.vega()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This approach allows to work with such a valuation object similar to an analytical valuation formula like the one of Black-Scholes-Merton (1973). For example, you can **estimate and plot present values, deltas, gammas, vegas, thetas and rhos** for a range of different initial values of the risk factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 6.64 s, sys: 954 ms, total: 7.59 s\n",
      "Wall time: 7.66 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "k_list = np.arange(26., 46.1, 2)\n",
    "pv = []; de = []; ve = []; th = []; rh = []; ga = []\n",
    "for k in k_list:\n",
    "    call_eur.update(strike=k)\n",
    "    pv.append(call_eur.present_value())\n",
    "    de.append(call_eur.delta(0.5))\n",
    "    ve.append(call_eur.vega(0.2))\n",
    "    th.append(call_eur.theta())\n",
    "    rh.append(call_eur.rho())\n",
    "    ga.append(call_eur.gamma())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a little plot helper function available to plot these statistics conveniently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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owA7a82lKLqWlJ7/Kd1paKIwd/7VdO4u2bRtXKHPT9/54sVT7+RrhEhEROS0e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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d3a97f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_option_stats_full(k_list, pv, de, ga, ve, th, rh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## valuation_mcs_american_single"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The modeling and valuation of derivatives with American/Bermudan exercise is almost completely the same as in the more simple case of European exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "me.add_constant('initial_value', 36.)\n",
    "  # reset initial_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "put_ame = valuation_mcs_american_single(\n",
    "                name='put_eur',\n",
    "                underlying=gbm,\n",
    "                mar_env=me,\n",
    "                payoff_func='np.maximum(strike - instrument_values, 0)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The only difference to consider here is that for American options where exercise can take place at any time before maturity, the inner value of the option (payoff of immediate exercise) is relevant over the whole set of dates. Therefore, `maturity_value` needs to be replaced by `instrument_values` in the definition of the payoff function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.452"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "put_ame.present_value()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since DX Analytics relies on Monte Carlo simulation and other *numerical* methods, the calculation of the delta and vega of such an option is identical to the European exercise case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6655"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "put_ame.delta()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.3122"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "put_ame.vega()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 15.5 s, sys: 957 ms, total: 16.5 s\n",
      "Wall time: 16.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "k_list = np.arange(26., 46.1, 2.)\n",
    "pv = []; de = []; ve = []\n",
    "for k in k_list:\n",
    "    put_ame.update(strike=k)\n",
    "    pv.append(put_ame.present_value())\n",
    "    de.append(put_ame.delta(.5))\n",
    "    ve.append(put_ame.vega(0.2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CAXz4f51G4UOpFQaKUKg27k52pJuQnFfyyk2IdPaTRi71Qztp1q7hIYHhcCGi\n/LHy+6q7PsaRFEycREKZAFhMC3qJiEhFIv2nqA/wJoBlWUuNMT3LHOsEbLQsazeAMWYJ0BeYHeEy\nHJFn/Tp20YnPOYsDJOMjQAJ+fP4AXiAlBRISbLxem4QE54+1s03Rdtn9B2/b+HyUeZRul/+M8tsZ\nGSnk5eWVbJd9n88HGRcNJGX9SnwE8BAqWUY82LkLu9/9pDa/fFVSdnyGd/06ghqfISIiRxDpUFIP\n2FtmO2SM8VqWFazg2H6g/tF8aEZGeuRK2LkzXVetYidNyu/v1g1Wrozcdaos9fCHHrgDrrjikN3e\ne/8vsl+bmnDLDc4D54etXnRLU+Ni/vsRAapjfFAd40O81THSoWQfUPYr5C4KJBUdSwf2HM2H5uTs\nj0zpgMTxE8uNKSm27/Y7KIzgdaoiIyP9yHUccCGJz04/dEbIgAshSmWuqkrrGAdUx/igOsYH1TF2\nHSlIRTqUfAyMAF4tGlOyqsyxbKC9MaYRkIvTdfOPCF+/UnV1yqdmhIiISLyLdCjJAgYZYz4BXMAN\nxpgrgTTLsp4zxkwC3gLcOLNvfojw9Y+K/sCLiIjEHpdt29Eug4iIiAhRXKJKREREpJRCiYiIiMQE\nhRIRERGJCQolIiIiEhMUSkRERCQmKJSIiIhITFAoERERkZigUCIiIiIxQaFEREREYoJCiYiIiMQE\nhRIRERGJCQolIiIiEhMUSkRERCQmKJSIiIhITFAoERERkZigUCIiIiIxQaFEREREYoJCiYiIiMQE\nhRIRERGJCQolIiIiEhMUSkRERCQmKJSIiIhITPBGuwCVCQZD9u7d+dEuRo1q2DAF1bHuUx3jg+oY\nH1TH2JWRke463LFqhRJjjBv4N3AaUAjcbFnWxjLHRwCTgSAw3bKs5yt7z2EL6PVUp4h1iuoYH1TH\n+KA6xgfVsW6qbvfNxUCSZVm9gT8AjxYfMMb4gMeBwUA/4BZjTLMjvae2ZW3IpN+s3jSf0pB+s3qT\ntSEzWkURERGRItXtvukDvAlgWdZSY0zPMsc6ARsty9oNYIxZAvQFeh/hPUeUkZFezWIeatbqWYx7\n+0bY2R7CHcjes5dxP0widWwKV51+ecSuU1WRrGOsUh3jg+oYH1TH+BBvdaxuKKkH7C2zHTLGeC3L\nClZwbD9Qv5L3HFFOzv5qFvNQD77/EGz5BUz/uNz+qx+GmxJt0tJsUlMhNdUmLa34+fCvS891Xpd9\nTkwE12GiaMW1AAAgAElEQVR7zkplZKRXWsesDZk8sexR1u9eR4eGHbmjx52Maj/6WL4Utepo6ljX\nqY7xQXWMD6pj7DpSkKpuKNkHlP1Ud5lwcfCxdGBPJe+pNet3r4NmSdD/PtjfHPxp4E/H5U+nc4N+\n5OZCXp6LH35wk5sL4fBRpIrD8HpLA0rZAFMceIr3NWsGLpevTKgpe9zmw5/nc9env4aEPHBB9q41\njHvnRoA6FUxERESOpLqh5GNgBPCqMaYXsKrMsWygvTGmEZCL03XzD8A+wntqTYeGHcnetQb6P1hu\nf6fGXXjr8k/K7bNtKCiA3FwXeXnOc26ui/z8Q/cVv87Lc5GbW/o6L88JOTk5Lr75xoXff7iQk3SE\nUo8teoQhZSc0Xg+NLe5dvofES7y0axemTZswCQnH8pURERGJruqGkixgkDHmE8AF3GCMuRJIsyzr\nOWPMJOAtnIG00y3L+sEYc8h7IlD+Krujx50lrQxlTeg+6ZB9LhckJ0Nysk1GBji56tj4/ZQEFSfQ\ngM+XytatBw4bfP7z1VzswjSnVSf3BNh6Nmw5h5+/guvnOZ/r8di0bm3Trl2YU05xHu3aOY+mTe2j\n6kYSERGJJpdtH/sf2hpmR7rPLGtDJk8uf6xkfMaE7pOi2g1SWb9gv1m9ndadYkEf7G7Lif7B3ND8\nETZtcrNxo5tNm9zs2HHohKr0dPuQoHLKKWHatg2TklITNTpUXe37rArVMT6ojvFBdYxdEV+npK4b\n1X50nRqLcUjrjjcAGRb3DPo9o9oHyp27Zw9s3FgaUoqf165189VXh85pb9ny0LDSrl2Yli1t3Frv\nV0Qk6ur6RIeqOC5DSV1T/MN3NK07DRpAz55hevYMl9sfCsGWLa5yQaX49Ycfevnww/Kfk5xsc/LJ\n4Qq7g+rVq7GqiohIGVkbMsv9p7TsRIdbMqo3CmL58i+ZPPlu2rQ5GYBgMMiYMVcwYMCgCs8fP/4W\nfve7P9KwYUOWLv2UwYOHVuu6R0OhpI441tYdjwfatLFp0ybEgAGhcsdyc2HzZvdhWlgObV3JyDi0\nZeWUU8KcdJKN96CfqOMp4YuIRNoTyypeZ/TJ5Y9xyy+qPzSzR4+ePPDAXwHIz89n/PhbaN26Ne3b\nm8O+Z+PGDXz88QcKJVKz0tKgW7cw3bqVb12xbfjpJ9chLSsbN7pZutTDp5+W//Hxem3atCkOKTb7\n0j/nxe3ToMl2SAlpKrOISBWt372uSvurIyUlhYsuuoT331/M4sXvsHLlCsLhMJdffhXnnz+w5LyZ\nM6ezceMGXn99Dl27duPppx8nHA6zZ88efvvbP9C162nHXBaFEjkslwtatLBp0SJE377lW1cKCuCb\nbw5tWXFCS3HrSh9gifMyeQdkrIWMtUxetY1GYz0YE6ZZM80MEhE5nJJlLCrYH0mNGjVi1qyX6NDB\nMGXKNAoLCxk37gbOPPPsknOuvfZGXn/9NS666BIWL36b8eMncsop7Xj77TdZuPANhRKJnqQk6NQp\nTKdOh7au7NjhjF25aOoE7B3tYUdH57HlHPi+L9uXwZjXnPPr1bPp0CGMMaGi5zAdOjgDbRVWROR4\nV5VlLI7Ftm3bGDx4GG+9tZDx428BnLEm27b9WOH5TZo0ZcaMqSQmJpKfn09qampEyqFQIhHlckFG\nhk1GRoiO335K9q6ppQcDibCzAy0LhnB5o4dYv97N+vVuvvrKzZdflh+7kprqhJXiR3Foad1as4JE\n5PhRlYkO1ZWXl8sbb2QxfPjFnHFGT37/+/8jHA4zY8ZUWrZsVXKe2+0mHHaWEXnyyb8zefJDtGlz\nMtOmPctPP1UcXqpKoURqzCEJ31cIJ6xi8qCJjGrvL9nt9zsDbdevd2NZ7pKwsnq1mxUryoeV5GSb\n9u3D5VpVjAlx0kk2nvi7i7eISI0sY7Fs2ZeMH38LHo+HUCjETTeNo2/f8/jnPx/nV7+6mQMH8unb\n9zxSUkpbQFq2bMXmzRt59dX/MHjwMO699/ekp9cjI6Mpe/fuiUi5jsvF02JNXV0A52gcy0J1wSB8\n+60Ly/KUCywbN7opKCjft5OY6CwQVxxUikPLySeH8flqomaHiufvYzHVMT6ojvGhrtZRi6dJ1BQn\n/Or84/F6oV07m3btglx4Yen+UAi+/95VFFQ8JS0r69cfOoXZ63XCStmg0qGDM4U5MbHi62oas4hI\ndCiUSJ3j8cDJJ9ucfHKIIUNKZwWFw/DDD65yrSqlrSyegz7Dpk0bmw4dQmW6gcKs5TV+/VHFCxUp\nmIiI1CyFEokbbjeceKLNiSeWXyDOtmHbNleZoFIaWBYt8rFoUZkPcV0NDc4pmb7MCV/BCSt44ssn\nFEpERGqYQonEPZcLmje3ad48RP/+5cNKTk75lpX/9/4n8HNnWD/CeRTJ9uVxwYtJdO0aomvXMF27\nhujY8fBdQCIiUnUKJXLccrmgaVObpk1D9OnjhJWls8Y7CxXlNYafu8C202HbGSTm9GbFivblpi57\nvc605eKQcu650KoVpKdHq0YiInWbQolIGSXTmFN3wskfOA/gqUHTGXZic9atc7NqlYdVq5zn7Gxn\ncO0rrxRP8UmnTZtwSYtKly7Oc7NmMT/LTUQk6hRKRMqobKGi008Pc/rppavYhkKwaZObVavcbNqU\nzGefBVm92sMbb/h4443Sz83IKG1RKQ4rbdpoITgRkbIUSkQOUpWFijweSqYbZ2RATs4BbBt+/NFV\n0pqyapWb1as9vPeel/feK/0nl5Zml7SkdO0aoksXZwZQba2rIiISa6oVSowxycBLQFNgP3CdZVk5\nB50zERhbtLnQsqwHjDEuYCuwoWj/p5Zl3V2tkovEKJcLWra0adkyxNChpQNrd+2C1atLu35Wr3bz\n+eceli4t/WeYkGDTsWNpSOnaNcSpp4aJ0G0lRERiWnVbSm4DVlmWdb8xZixwDzCh+KAxpi1wFXA2\nEAaWGGOygHxguWVZIyr4TJG41qgR9O1bfMflAAD5+bB2bWlIKR6n8vXXpQNqXS5nATin26e0C6hx\n4/LjVLTom4jUddUNJX2AR4peLwLuPej4FmCoZVkhAGOMDygAegAtjTHvAweAiZZlWdUsg0idl5IC\nPXuG6dmzdJxKIAAbNrhLun2Kn7OyPGRllb63RYtwyfiU/CZLmLL9fqj/Pbi06JuI1E2V3vvGGHMT\nMPGg3duB8ZZlZRtj3MD3lmW1quC9LuDvQLplWeOMMX2BZpZlzTbG9AEetyzrzErKqGkLctyzbfjm\nG1ixwnl89ZXz/OPBN+ZM2gUnfgrdXoSOr9OtVQdW3royKmUWETmM6t/7xrKsacC0svuMMXOA4tUY\n0oFDbg9ojEkCpuOMOflV0e4vgWDR5y4xxrQwxrgsyzpi8KiLNxyqirp6U6WqUB2PXXo69O3rPIr9\n/LOL1avdXDH1IeyfToOfusOGC51H4h5WdX2VRSfl0aNHGNdhfw0cPX0f44PqGB/qah0zMg6/mFN1\nu28+Bi4APgeGAR+VPVjUQvI68J5lWQ+XOXQfsBN4xBhzGrClskAiIofXtKnN+eeH6PjzPLJ3/dXZ\nmWNg5XWw8lrsL2/hggugXbsQY8cGGTMmQPPm+icnIrGp0u6bihhjUoAXgOaAH7jSsqxtxphJwEbA\nA/wXWFrmbXcD63Bm7aThtJjcblnWukouZ9fFJFgVdTXtVoXqWLOyNmSWjCEpEXbzmwYL2fLR+Sxc\n6KWw0IXbbdO/f4ixYwMMHRokKalq19H3MT6ojvGhrtYxIyO9+t03FbEsKx8YU8H+x8psHu7X3YWH\n2S8i1XT4Rd9+AVcXsHcvzJ3rY9YsX8l6KfXr21x8cYCxYwN07x6Z7h0RkWNRrZaSWqaWkjigOsaO\nDRvcvPKKl1df9bFtm7OkbPv2IS6/PMhllwU44YTD/06oK3U8FqpjfFAdY9eRWkq0yLXIcaZ9+zD3\n3ONnxYo8Zs3KZ9SoAN9/7+ahhxI5/fRUxo5NZu5cLwUF0S6piBxvtMy8yHHK44Hzzw9x/vkh9uxx\nundeeUXdOyISPWopEREaNIDrrw+waFE+S5bk8etfF5KUZPPCCwkMG5bKueem8PTTCYeuiyIiEkEK\nJSJSTocOYe69t7R75+KLA3z3nZs//SmRE0+EK65I5vXX1b0jIpGn7hsRqZDXe2j3zmuvJbF4sZfF\ni53unVGjnO6dM85Q946IHDu1lIhIpYq7d5YupVz3zowZCQwdWtq9s22bkomIVJ9CiYhUyZG6d04/\nPVXdOyJSbeq+EZFqObh7JyvLmb1zcPfOFVcEOP10de+ISOXUUiIix6xBA7jhhgBvvpnPRx/lMX58\naffOkCGp9O2bwj//6WP7diUTETk8hRIRiShjwkye7HTv/Pe/+Vx0UYBvvnHz4INJnHZaKldemcy8\neaXdO1kbMuk3qzfNpzSk36zeZG3IjG4FRCRq1H0jIjXC64UBA0IMGBBi9+7SxdnefdfLu+96adDA\n5rTz1/FB439DizXgguxda0puLFh8Px8ROX6opUREalzDhod27yQk2HwwpxM8/wX8ezW8+xdYNxL2\nN+PJ5Y9V/qEiEnfUUiIitaq4e+ePf/TT6q4rCK+4BtZdDEvuLjlnbYNvuWVxEj16hOjRI0TXrmES\nE6NYaBGpFQolIhIVXi+Ys74lu91YKEiHH86Crb1gay88P57D3Lk+5s71AZCQYNO1a5ju3UMlQaV1\na1szekTijEKJiETNHT3udMaQJO2HUxY7D+BfA6dzhm8My5Z5Sh4rV7pZtszD8887723SJEzPniF6\n9HDCyhlnhEhLi2JlROSYKZSISNQUD2Z9cvljrN+9jg4NOzKh+6Si/TYnnxxk9OggAAcOwKpV7nJB\n5c03fbz5pvNZbreNMcVBxQkr7duHcWvknEidoVAiIlE1qv3oo5ppk5wMZ50V5qyzwkAAgJ9+crFs\nmYfly52w8tVXHrKzPbz4ovOe9HSbM84IlQSV7t3DNG5s12BtRORYVCuUGGOSgZeApsB+4DrLsnIO\nOudJoE/RcYCLAH9l7xMROVrNm9sMHx5k+HBnOxCAdevcfPmlh+XLPSxb5ubDD718+GHpr7qTTw6X\njEvp0SNE585hEhKiVAERKae6LSW3Aassy7rfGDMWuAeYcNA5PYAhlmXtKN5hjJl0FO8TEakWnw+6\ndg3TtWuYG25wWlN274YVKzxlgoqHzEwfmZnOINqkJJtu3Zzunp49QwwejGb6iERJdUNJH+CRoteL\ngHvLHjTGuIH2wHPGmGbANMuyplf2PhGRSGvYsPQePQDhMGze7OLLLz3lxqd8/nnpr8MTTkgtaUnp\n2TNMt24hUlJKPzNrQyZPLHu0ZBzMHT3u1GJvIhFQaSgxxtwETDxo93Zgb9Hr/UD9g46nAk8DjwEe\n4H1jzJdAvUreV6GMjPSjOa1OUx3jg+pYNzRrBr17l27n5cGyZbB0afHDzYIFbhYscFpTPB7o1g16\n9QJaLWXKT3+FxhvKrUJbr14yY7uMjU6FqiEevo+VUR3rnkpDiWVZ04BpZfcZY+YAxV+JdGDPQW/L\nB560LCu/6Pz3gNOAfZW8r0I5OfsrP6kOy8hIVx3jgOpYt3Xq5Dzuuiudn3/ez48/OoNoi1tUvv7a\nzYoVLqAXsB6Sd0KrpdBpDnR6jT/9788MaHZhtKtxVOL5+1hMdYxdRwpS1e2++Ri4APgcGAZ8dNDx\nDsArxpgzcJay7wO8gDPA9UjvExGJOpcLWra0adkyyMiRzpRkvx/WrnUz5Im7sbcULfS24ULnseBf\nZJsFLEjzMnBgUGNSRKqpuqFkCvCCMWYJzoyaK6FkIOtGy7LmGWNeBJbizN2baVnWGmPMNxW9T0Qk\n1iUkwOmnh+k49D2ydz3t7Nx9Eqy+Ar6+GnvtpdxwA9SvbzNyZIBLLw3Sq1dI66SIVIHLtmN+zr5d\nF5unqqKuNsFVheoYH1RHZ5Br8Z2MS9hwT5u57PpiGHPmeNm2zUkiLVuGueQSJ6B07hyuyWJXib6P\n8aGu1jEjI/2wN4hQhhcRqYJR7Ufz7KDpdG7cBa/bS+fGXXh28HR+c+H53H9/IStW5PHaa/lccUWA\nfftcPP10Iv37p9K/fwpPP53ADz/ohj0ih6OWkhhQV9NuVaiO8UF1rJoDB+Ddd73Mnu1l8WIvgYAL\nl8vmF78IcemlQUaMCFD/qOYgRpa+j/GhrtZRLSUiIlGQnAwjRgSZObOA1atz+cc/Cjj77BAff+xl\n0qQkTj01jRtuSGL+fC+FhdEurUj06d43IiK1oGFDuPbaANdeG2DLFhdZWT4yM70sWOBjwQIf9evb\njBjhjD/p3VsDZOX4pB97EZFaduKJNr/5jZ8PPsjnvffyuP12PykpNi+9lMCoUSn06JHKgw8msGaN\nfkXL8UU/8SIiUeJyQZcuYe67r5Dly/OYMyefK6/0s2+fi3/+M5HzzkulX78UnnpKA2Tl+KBQIiIS\nAzwe6NMnxBNPFLJmTS7Tph1g2LAAmza5eeihRM44I42LL07mxRd97DmqtbBF6h6NKRERiTFJSc4A\n2REjguzZA2+84Yw/+eQT53H33YkMHBjk0kuDDBoUJCkp2iUWiQyFEhGRGNagAVxzTYBrrgmwdauL\nOXN8vPaal4ULfSxc6KNevdIBsr/4hQbISt2mH18RkTqiVavSAbLvv5/H+PGFpKXZvPxyApdckkL3\n7qk88ECiBshKnaWfXBGROujUU8NMnuxn+fI8srLyufpqP7m5Lv71r4RyA2S3bi0dIJu1IZN+s3rj\nfdBLv1m9ydqQGcUaiBxKK7rGgLq6Kl9VqI7xQXWMbQUFzgqymZle3n3Xi9/vBJLevYO0PfczXnYN\nh+Tyo2SfHTSdUe1HR6O4Naoufx+PVl2t45FWdNWYEhGROJGUBMOHBxk+3BkgO39+6QDZTz89Bzzb\noP1C6Pof5zkhnyeXPxaXoUTqJnXfiIjEoQYN4OqrA8yde4AVK3JxDfoDNLZg3SiYPRseyYFZr7Hu\nf2ewb1+0SyviUCgREYlzLVvadBwxH351GtzaDfr+CRp8C+suIfzaTDp3TuOqq5L573+97N4d7dLK\n8UzdNyIix4E7etzJuHduhBNWOY/zJ8PPnRjpf4lNn57GO+94eecdL16vzTnnhBgxIsiwYUEyMmJ+\n3KHEEYUSEZHjQPG4kSeXP8b63evo0LAjEwZNYlT79kA+mze7mD/fx4IFXj74wHncdZdNr14hhg8P\ncuGFQZo3V0CRmqXZNzGgro6grgrVMT6ojvGhsjpu2eJiwQIv8+d7+fzz0v+79uwZYsSIABdeGKR1\n69j+26HvY+yK+OwbY0wy8BLQFNgPXGdZVk6Z46cDT5R5Sy/gYuAtYCuwoWj/p5Zl3V2dMoiISM04\n8USbW28NcOutAbZtcwLKggVePvnEw5dfJnHffXDaaU4Xz/DhAdq2je2AInVHdbtvbgNWWZZ1vzFm\nLHAPMKH4oGVZXwH9AYwxY4AfLMt60xjTDlhuWdaIYyu2iIjUhhNOsLnppgA33RRgxw4XixY5LSgf\nfeRh5cpEHnookU6digNKEGPCuHRDY6mm6s6+6QO8WfR6ETCwopOMManAA5QGlh5AS2PM+8aYhcYY\nU83ri4hILWvSxOaaawK88soB1q7N5amnDjBkSJDNm9088kgiffumcs45Kfz1rwmsWuUm9kcHSKyp\ndEyJMeYmYOJBu7cD4y3LyjbGuIHvLctqVcF7fwM0tizrvqLtvkAzy7JmG2P6AI9blnVmJWXUj7WI\nSAzbtw8WLIDXXoOFC+HAAWd/27Zw6aXO46yzUAuKFDvsT0K1BroaY+YAf7Ms63NjTH3gY8uyulRw\n3mfAaMuythRtpwBBy7L8Rds/AK0syzpSITTQNQ6ojvFBdYwPNVnHvDx47z1nDMrbb3vJzXX+/rRo\nES5ZbfbMM0N4PDVy+RL6PsauIw10rW73zcfABUWvhwEfHXxCUVhJLA4kRe4D7ig6fhqwpZJAIiIi\ndUhqKowYEeSZZwpYuzaXF1/M5/LLA+TluXjuuQRGjkyhW7dU7rorkQ8/9BAMRrvEEkuqO9B1CvCC\nMWYJ4AeuBDDGTAI2WpY1D+gAfHvQ+/4GvGSMuRAIAtdX8/oiIhLjkpJgyJAQQ4aE8PthyRIPCxZ4\nWbTIy4wZCcyYkUCjRmGGDXNaUM49N0RCQrRLLdGkdUpiQF1tgqsK1TE+qI7xIdp1DAZh6VIP8+c7\n3TzbtzuN9vXq2QwZ4gSU/v2DJCc752dtyOSJZY+WLPp2R487K72JYLTrWBvqah11l2AREYkZXi/0\n6ROiT58Qf/lLIV98URpQZs/2MXu2j5QUm8GDgzTtsYTnDoyHhHwAsnetcZbLB93dOA4plIiISNS4\n3XD22SHOPjvEgw8W8tVXbubP9zJ/vo+5c30w9zzw7oB2i6DLK2Dmga+AJ5c/plASh3SXYBERiQku\nF5xxRph77/WzdGke772Xh6vfQ9BwM6y7BDJfgX9sg9ensm5ZM8LhaJdYIk2hREREYo7LBV26hOl4\n6Sy4vQv8qjOc+2dI2gMrbiI84126d0/lT39KYN06/SmLF/pOiohIzLqjx53Oi6bZMOAemHAyXN+P\nPiMscnNdPP20s5LsgAEpTJniY/t2rdBWlymUiIhIzBrVfjTPDppO58Zd8Lq9dM44lWd/eT1zprVg\n9epcpk49wNChAbKz3dx3XxKnnZbK5Zcn89JLzkJuUrdoSnAMqKvTuqpCdYwPqmN8iMc67tzp4vXX\nndk7y5Y5y8WmpNhceGGQ0aMD9O1b86vI1ra6+n2siRVdRUREYkbjxjY33hhg0aJ8li7N5b77ICPD\nZvZsH5dfnsLpp6cyeXKibhQY4xRKREQkrrRta3P//fD553nMn5/H9df78ftdPPNMAgMGpNKvXwpP\nPZXAjz9q/EmsUSgREZG45HLBWWeFeeSRQlatymXGjAMMHx5g82Y3Dz2UyBlnpHLJJcn8979e9te9\nXpC4pMXTREQk7iUkwAUXBLnggiB79sC8eT4yM70sWeI8fv97m6FDg4wZE6B//xA+X7RLfHxSS4mI\niBxXGjSAa68NMG/eAb74Ipe77y6kVaswc+f6uOqqFE47LZU//jGRFSs0/qS2KZSIiMhx66STbCZO\n9PPxx/m89VYev/ylH4CpUxMYMiSVc85J4bHHEvj+e40/qQ0KJSIictwrXuL+z38uZOXKPF5+OZ9R\nowJs3ermb39LpGfPNEaMSGbmTB979kS7tPFLY0pERETK8Plg0KAQgwaF2L8f5s/3kpnpY8kSD599\n5uWPf0xk0KAgY8YEGTgwSEJCtEscPxRKREREDiM9Ha64IsgVVwT54QcXc+Y4A2QXLPCxYIGPhg1t\nRo4MMGZMgDPPDONSL88xUfeNiIjIUWjZ0ubXv/bzv//ls3hxHrfd5ichweaFFxIYPjyVs85K5eGH\nE9i82UXWhkz6zepN8ykN6TerN1kbMqNd/DpBoURERKQKXC7o2jXMAw8U8tVXebzySj5jxgTIyXHx\n6KOJ9OqVxrjLOpH9Zj9C+xuRvXMN4965sU4Ek2iHqWO6940xZhQwxrKsKys49ktgHBAEHrIsa74x\nJhl4CWgK7Aeusywrp5LL6N43cUB1jA+qY3xQHWtGbi4sWuTlrqeXkWf1Brv4Zjth8BbgSfDTtH49\nEhMhOdkmKQmSkmwSE53n5GTK7St7Tvln5/UJJ6RQUJBXsp2cDImJpedUtSspa0Mm49658ZD9zw6a\nzqj2o4/9C1TkSPe+qfaYEmPMk8AQ4KsKjp0A/AboCSQBS4wx7wC3Aassy7rfGDMWuAeYUN0yiIiI\nxIq0NBgzJshvdvSHfRmweixsGgT+NAgmEQqmkJjYmYIC2LPHTWEhHDhwrINQUg97pDjEFAeVg4NQ\n6bZzzhvfuSH0EHgPQOslcPIHADy5/LGIhpIjOZaBrp8Ac3FaQw52FvCxZVmFQKExZiPQDegDPFJ0\nziLg3mO4voiISMzp0LAj2fYa6P2E8yjSuXEX/nf5J+XOtW0oLISCAigocB3mufT1gQOuovNduN2J\n7NzpL/f+Awec5+JzircLCmD/flfJPtuuKAxdV/qySTaM7wzA+t3rauLLVKFKQ4kx5iZg4kG7b7As\n6xVjTP/DvK0esLfM9n6g/kH7i/dVKiMj/WhOq9NUx/igOsYH1TE+RKuOk8+7hyteu+KQ/ff2/78a\nKFPV5yPbNvj9FIWc0sdFL17Oxp+3QiAZGm8oOb9zRuda+1pWGkosy5oGTKvi5+4DytYgHdhz0P7i\nfZVS32fdpzrGB9UxPqiONWtAswt5dtB0nlz+GOt3r6NDw45M6D6JAc0ujGiZIlFHj8fpdkpLg9+N\nGFrhmJLbu90R8XIfTk2tU/I58GdjTBKQCHQCVgMfAxcUHR8GfFRD1xcREYmaUe1H19o4jEgpLu/B\nYao26xHRUGKMmQRstCxrnjHmKZzQ4Qb+z7KsAmPMFOAFY8wSwA8cMmtHREREoiPaYeqYpgSLiIiI\nRIoWTxMREZGYoFAiIiIiMUGhRERERGKCQomIiIjEBIUSERERiQkKJSIiIhITFEpEREQkJiiUiIiI\nSExQKBEREZGYoFAiIiIiMUGhRERERGKCQomIiIjEBIUSERERiQkKJSIiIhITFEpEREQkJiiUiIiI\nSExQKBEREZGYoFAiIiIiMUGhRERERGKCQomIiIjEBIUSERERiQkKJSIiIhITvNEuQGWCwZC9e3d+\ntItRoxo2TEF1rPtUx/igOsYH1TF2ZWSkuw53LOZbSrxeT7SLUONUx/igOsYH1TE+qI51U8yHEhGR\nWLN3byYbN/ZmzZqGbNzYm717M6NdJJG4EPPdNyIisWTv3ky2br2xZLuwcE3Jdv36o6NVLJG4oFAi\nIse9ggLYu9fFvn0uNm2C777zsHevq8yj9PhPP3Vg376l5OU1oLAwmRYtNtGmzZr/3959h0dV7H8c\nf4Ezo2MAACAASURBVG+2khACmKWLIFwGFS4lCFIuTUGUoiICSlEDKAICAtJBBBQFIVhAlCYYkWbn\nJ4iKUkUFRb14GeCChWuLlIS07b8/TgKhRBCS3c3m+3qePE/2ZM+emZyc7Gdn5sxQo8b/+Ne/zCjl\n54orAqGukhBFkoQSIURIpaauJSVlNi7XPuz22jidI/92i4PbnRsa4MQJ06kAkRsq0tI4Z1veoOFy\nnT3uLvovjtYcmy2LkiVPYLF4+OabVuzZ0waA2bONZ8TH+6ld20+tWn6UMr5XykfZsn+rWkIUOxJK\nhBAhk9sV4vOZOXmyDOnpLr75Zj4ORyV8vpanwkNamokTJ/IPGllZ+Q7mPy+rNUBcXIC4OLjySj+l\nShmPS5UKUKmSDavVdWpb7va4OChVKsCff7YEvj71WtnZJfjpp9ocOXIzJ05MQWsz+/ZFsW2bhW3b\nzjyu02mElNyv3LBSpkwB/DKFiAASSoQQQefxwDffRPHOO2ns2rWRf/+7OS7XX7VOnMliyQ0LULHi\n6VBRurSx7XSQODNUGD8P4HCAKZ8c43TaSElx53tsh+PhM8aUOBxZ1Kr1NW3bPkxc3On9MjLg4MEo\n9u2LQusotDajdf5hxQgoeb8krIjiR0KJEKLQ+Xzw739HsW2bmW3bLOzcaSYjwwQMA6B69e+48kpN\nyZIncr7S+Mc/xudpwSBP6AgQHZ1/qChsuV1LKSlz8nQ5jTinyykmBurV81Ovnv+M7RkZcOBAblgx\ns3+/EVq2brWwdeuZxypXLm+LitEdVLu2j9KlC7WKQoSMhBIhRIHz+8npwjCzbZuZzz6zkJp6OkXU\nrOmjRQsfNWuO5brrXqV06T/P2N9ur0PNmo8Gu9gXLS6u2yXfaRMTA/Xr+6lf3w94T21PTzfCitZR\n7Nv312GlfPnTYeX0uBUfcXGXUSkRtgpi3FVRIaFECHHZAgGjqyI3hOzYYebo0dPTIF11lZ9OnTy0\naOGjeXMfFSoYd6ekptblyJE/z3k9p3NE0MoeLkqWhAYN/DRocG5YyQ0ouV1AWkexZYuFLVvOfI0K\nFXJbU053ASnlPxVWct/c9u6N/De3SPFXt6A7nfdf0msOGfIA998/gISE609tmzv3GWrUqEnnzrdf\nXoEvk4QSIcTfFgjAjz+acsZHmNm+3czvv58OIZUq+ene3UOLFl6aN/dx5ZXnv0X2YrtCirOSJaFh\nQz8NG54bVrSOYv9+o2Xlr8JKxYp+rr76VypWPEG1ajdw7bVQvbrMr1IUpKTMzmf7HGrWvLRQ0rnz\n7WzY8H+nQonH42H79q08+ODgSy5nQZFQIoS4KP/7n4n162H9egfbtpk5cuR0CHE6/dxxR25LiJfq\n1QMXPebjcrpCirOSJSEhwU9Cwplh5eTJ0y0ruWFl//4otm+vDDxy6nm1a39Bx44L6dBhAfXqye8/\nXLlc+/7W9ovRuvWNvPTSPLKzs3E4HGzdupnGjZvwyy//Y+7cWQQCAeLi4hg37jFiYmKYPftptP6e\nsmWv4Ndff+Hpp5PIysrk+eeT8Pv9nDhxglGjxlK3br1LLlMuCSVCiPP6/XcT27cbrSDbtlk4fDg3\nhFgpUyZAp04emjf38a9/+fjHP/whG3gqzhQbe/6w8sUXVfnxR8Xhw3XYsaMLO3d2ZN++xsybl063\nbjZ69/bQoIGcx3Bjt9fG5dp73u2X/pp2WrZszZYtn9C+/S28//67PPDAIJ5+ejrjxk2mevWrWbfu\nbV57bRnXXnsdaWmpLFy4nOPHj3P33XcAcPjwIYYMeYQaNWqyceMG3n//PQklQoiCc+wYbN9uyQkh\nZvbvP73YV2xsgJtv9tKhg4V69TK49lo/UbJyVpFStmxlYmI+59prP6djx8WkpFRm/fr7Wb9+IMnJ\nlUlOtnHttT769PHQrZtHBs2GCadz5BljSk5vv7xxV50738G8ec/SoEECJ0+epFat2vz442Fmz34K\nAJ/PS5UqVfnhhx+oU6cuAGXKlKFq1WoAxMeX45VXFmG328nMzCQmJuayypNLQokQxVRaGnz2mfnU\nuJC9e0+HkOjoAG3benNaQrzUrevHbAanM5aUFP9fvKoIV2e/uTmd/6Nv3+mMGVODPXu6k5xsZcMG\nC+PGOZg61U7nzl569/bQpIlPWk9CqLDGXdWoUZOsrAzWrFlJx45dAKha9SomTpxKhQoV+PbbPRw9\n+ic2m50PPnif7t0hLS2Nn3/+CYBnn53F5MnTqVatOosXv8Svv/5yeRXNIaFEiGIiPR2++MJ8aq6Q\nb7+Nwu833m0cjgD/+pf31JiQBg38WK0hLrAoUHnf3NzufdhsuW9ud9K2rY+2bX388YeJVausJCdb\nWb3a+KpVy0evXh66d/fKmj4hUljjrjp27MK8ec/xxhvrABg5chzTp0/G5/NhMpkYO3YSV15ZlZ07\ndzBwYCJly16Bw+HAYrHQvv0tTJo0htjYUjid5UhNPVEgZTIFAmH/RxZISTkZ6jIUKuPTp9SxqAt1\nHc+eyyA2djT793c7FUK+/joKr9cIIVZrgIQE36kxIQ0b+nA4LnyMUNcxGKSOxt1V27ebSU62sm6d\nBbfbhM0W4NZbjdaTFi18Yd99J+exYPz44w8cOKC56aabSU09QZ8+PVi79j1sNtslv6bTGZtv25u0\nlAgRAXLnMjh0qA5bt47n66/b8v33TfF47ACYzQHq1/efukX3+ut9FFAXsIhAJhO0aGFMcHfsGKxZ\nY+XVV628/bbxVa2an969PfTo4aF8+bD/YCsuQ7ly5XnxxedYvfp1/H4/Dz308GUFkguRlpIwIIk+\nMoSqjh4PLF36GKtX386337YEwGTyU7Pm1zRq9B2dO3enSRMfsbGXfyw5j5HhUuoYCBjdf8nJVt59\n10JWlgmLJUD79l769PHQurUPs/nCrxMsch7DV0hbSpRSTYCntdatlVL1gecBH+AC+mqtfy/sMggR\niX7/3URyspVly6z89tscABo1+oBOnRbSsOHHxMaeACxcd92doS2oiAgmEzRp4qNJEx/Tp8Mbbxhj\nT95/3/iqUsXP3Xd7uOceD5Urh/2HXRGmCrVXUCk1GlgE5PZWPws8rLVuDbwJjCnM4wsRaQIB+PLL\nKAYOdNCwYQxPP20nI8PEXXcls2yZYtasDrRq9UZOILm8uQyEyE9cHCQmevj440w2bsygTx83x4+b\nmDXLTkJCDL16lWD9egte74VfS4i8CrX7Ril1J/At8KrW+galVEWt9a85PxsMVNZaj7/Ay0jkFsVe\nVhasXAkvvABffWVsu/ZaGDIEeveGzMyV/Oc/d5+z3zXXvE758j2DXFpRHKWnG3+jCxfCF18Y2ypW\nhMRE6NcPqlcPbflEWMm3+6bQx5QopaoBK7XWN+TZ1gxYDLTUWqdc4CVkTEkEkDpemp9+MvHKK1Ze\ne83G8eMmoqIC3HKLl379jNlU884fYdx9U7hryMh5jAyFXce9e6NITrayZo2VtDTjj7RVK2PsSYcO\nXgpxnOQpch7DV1jdfaOU6gFMADpeRCARotgJBGDLFjOLF1vZuNGC32/iiiv8DB/upm9fD1Wq5L+4\nnawhI8LBddf5mTHDxaRJLt57z0JyspXNmy1s3mwhPt5P9+5e+vRxU6OGNISLMwU1lCilegMPAq21\n1seCeWwhwt3Jk7B6tZUlS6wcOGDcxtCggY9+/dx06eK9qHlEhAgn0dHQo4eXHj287N8flTMpm4X5\n823Mn2+jaVOj9aRTJ/n7Foagdd8AzYEU4Ccgd+q3zVrrxy7wEtJ9EwGkjvnbvz+KJUusrFplJSPD\nmKTqttu89OvnzlmuPnzIeYwMoayjywXvv2+0nmzdanwuLl06wF13eejd28M11xTM37ycx/AV0u4b\nrfUPQO54krKFfTwhigKfDz74wMLixaf/MVeq5GfYMDe9enlwOqVZW0Qmux3uuMPLHXd4OXTIxIoV\nVl5/3crChTYWLrSRkOCjTx83t93mlQn+iiGZ0VWIIDp61MRrr1l55RUrR44Yd+S3aOElMdEYAGiR\nK1IUI1dfHWDiRDdjxrjZuNFoPdm0yczu3SWYODHAnXd66NPHw1VXrT5jCQWnc6SMn4pQ8i9QiCD4\n5psoFi+28dZbFlwuE9HRAe67z01ioofatcOri0aIYLNaoWNHLx07evn559OtJ8uW2Vi2zMY//vFP\nOnVqQbt2PwB7T612LMEk8oT5kkpCFF0uF6xda+GWW6Jp1y6GlSutVK4cYPr0bL75Jp2ZM10SSIQ4\ny5VXBhgzxs3u3Rm89lomLVps4r//rUdS0gLuvfc/bN58J4GAsdqxiDzSUiJEAfvlFxPLl1tZvtzK\nn39GYTIZ64MkJrpp3Tr8V1cVIhyYzdCunY9Kldrz55/lePvtwaxePYopU9bSqNEHDB36CDVrhrqU\noqDJv0chCoAxtwj07+8gISGGOXPseL0mBg1y8/nnGSQnZ9G2rQQSIf4uu7028fG/0r//RJYuvY7G\njdeza9fN9Ou3hxkzbGRmhrqEoiDJv0ghLkNGBixfbqV162hatYJ337VSu7afpKRs9uxJZ8oUF9Wq\nyZ00Qlwqp3Pkqe8rV/4vTz11K48/3pX4eDdJSXZatoxhw4YwWp5YXBbpvhHiEhw6ZGLpUhuvv25M\no22xBOjRA3r1yqRJkzOnfxdCXLrcway5Syg4HLW5557O9O0bYM4cFy++aKNv32jat/fyxBPZXHWV\nfAgoyiSUCHGR/H745BMzixfb+PhjM4GAiXLl/DzwgDH9e926JUlJ8YW6mEJEnPyWUJg0yU2PHl7G\njrWzcaOFLVtiGDbMzeDB7hCUUhQECSVCnMVY2O70nAg22zjef/9Oliyx8cMPRo9n48bGongdOwZn\ncTEhxPnVquXnjTeyePNNC489Zufpp+2sXm3lxRehYcNQl078XRJKhMgjNXXtqTkQDh2qw1tvDeGj\nj24nO9uBwxGgVy9jbpG6deVWXiHChckEd97ppX17LzNn2lm0yEqHDtCpk4Np01xUrixdOkWFhBIh\n8khJmc333zdh+fLJfP75rQBUqHCYO+98k4cffoCyslCCEGErNhamTXPRo4eHSZNiWLfOyqZNFkaO\ndPPgg25p1SwC5O4bIXLs3Glm6NAkBg/eyeef30q9ep/yxBOdSU6uSbduYyWQCFFE1KnjZ8sWeO65\nLKKjA0ybZqdt22i2bZO7dMKdhBJR7O3YYaZr1xJ06RLNrl3tSEj4kLlzWzJ3bhuaNVuH2ezHbq8d\n6mIKIf6GqCjo2dPLjh0Z3HefmwMHoujaNZqBAx38/rvcHheuJJSIYsmY7MzMbbeV4Pbbo9m2zULb\ntl5Wrfo/nnmmPfXqbT3j+U7niBCVVAhxOUqXhpkzXXzwQSYNGvh4800rTZvG8NJLVrzeUJdOnE1C\niShWAgHYtMlMp07RdOsWzWefWWjXzsuGDRmsXJlFmzYtqVJlCXZ7HcCC3V6HKlWWyMJfQhRx9ev7\nef/9TGbNysZigUmTHNx0UzSffy5dOuGk0Ae6KqWaAE9rrVsrpWoCrwAB4N/AYK213MYgCl0gAB99\nZGb2bDtffWX8E+rQwcPIkW7q1TvzTzC/ORGEEEWb2Qz33mvcyj99uo0VK2x07hxNz54eJk1y4XTK\nXTqhVqgtJUqp0cAiwJGzaQ4wUWv9L8AE3FaYxxciEID16y20axdNr17RfPWVmU6dPHz8cQbLl2ef\nE0iEEJEvPj7A3Lku1q3L4LrrfKxcaaVZsxiWLrXik/kPQ6qwu2/+C3TN8zgB2Jzz/XrgpkI+viim\n/H547z0LbdtGc++9Jfjuuyhuv93D5s0ZLFmSLfOMCCFo3NjPhx9m8sQT2fj9MGaMg1tuiebrr2Vk\nQ6iYAoHCba5SSlUDVmqtb1BK/aK1rpSzvS2QqLXufYGXkPY0cdF8Pli7FqZNg717jRH4d98NEybA\nNdeEunRCiHD122/w6KOQnGxMxvbAA/Dkk8hUAIUj39ufgj15Wt6Pp7HAiYvZKSXlZOGUJkw4nbFS\nx8vk9cLbb1tISrJx4IAZszlAjx5ehg93UaOGkWtTUgrt8ICcx0ghdYwMf7eOZjPMmQPdupkZM8bO\nSy+ZWbvWz6RJLnr29BIVho0nRfU8Op2x+f4s2L/mr5VSrXO+vwXY+hfPFeKCvF5YudJCixYxDBpU\ngsOHo+jVy82OHRk8/3z2qUAihBAXo1kzH5s2ZfLYY9lkZZkYPrwEnTpF8913YZhKIlCwf8sjgceV\nUp8BNmBtkI8vIoTHAytWWGjaNIahQ0vw888m+vZ1s3NnBklJLqpXlzAihLg0VisMHuxhx44MunTx\nsGuXmXbtohk/3k5aWqhLF9kKvftGa/0DcEPO9/uBVoV9TBG5XC5YtcrKs8/a+PnnKGy2AImJbh5+\n2C2LbgkhClSlSgEWLcrmk088jBvnYNEiG++8Y2HKFBfdunkxycSwBU7ao0SRkJ0NS5ZYueGGGEaN\ncpCSYmLAADdffpnBU0/JKqBCiMLTpo2PzZszGDfORXq6icGDS3DHHSXYt0/eQgua/EZFWMvKgoUL\nrTRuHMPYsQ6OHTMxcKARRp54wkXFihJGhBCFz26HRx5xs3VrBh06eNixw5hyYMoUO+npoS5d5JBQ\nIsJSRga8+KKVRo1imDDBQVqaiSFDXOzalcHUqS7Kl5cwIoQIvqpVAyxfnk1yciaVKgWYP99G8+Yx\nvPuuhUKeYaNYkFAiwkp6Ojz/vI3rr4/hscccOaPfXezencHkyW6ZBloIERbat/exdWsGI0a4OHrU\nRP/+JejevQT//a8MNLkcEkpEWDh5EubOtdGoUQzTptlxu02MHOli9+50xo93c8UVEkaEEOGlRAkY\nO9bNli0ZtGnjZfNmC61axTBjho3ffnuLgwebsndvGQ4ebEpqqtxsejEklIiQSk2FZ56x0bBhSZ58\n0o7fb2LMGCOMjBnjpkyZUJdQCCH+2tVXB1i5MovFi7OIjw+QlGSnXbuWbNp0NeDD5drLkSOJEkwu\ngoQSERLHj8NTTxlhZOZMO2ZzgAkTjDAycqSbuLhQl1AIIS6eyQSdO3vZti2DXr0W8+eflZk48V3G\nj3+X3367CoCUlDkhLmX4k1AiClVq6loOHmzKp59aOHiwKYcPv8cTTxhhZM4cO3Z7gMmTs9m1K4Nh\nw9zE5j/7sBBChL2SJaF//wdZtKge9et/wmefdeb++/eyZs1wMjMPhLp4YS/Ya9+IYiQ1dS1HjiQC\ncOxYOVav7ss773QhO9uO0+ln9GgXfft6iIkJcUGFEKIA2e21qVZtL3PmtOXDD3szb14S8+cnsWlT\nf+bNi5JVyv+CtJSIQpOSMptjx8ozf/4z3HPPYVatGk3JkqkMHz6DXbsyeOghCSRCiMjjdI4EjC6d\n9u2TWbbsGtq1W86+fdfRvn00U6fayMwMcSHDlIQSUSj++MNEUlI/7rnnEGvWjKRUqaMMGzaI116r\nwW23TaZEiVCXUAghCkdcXDeqVFmC3V4HsFC+fAXmz/exalUmlSsHeOEFOy1bxvDpp+ZQFzXsSPeN\nKFB//mnihRdsvPKKlczMR3A6f6Z37xF06LAUm80NkHOhCiFE5IqL60ZcXLcztrVp42PLlgxmzbKz\nYIGV7t2juesuD1OnumTagxwSSkSBOHrUxLx5VpYssZGZaaJiRT+jR++kadPWp8JILqdzRIhKKYQQ\noRUdDY895qJrVw8jRjhYs8bKxx+bmTrVxV13ySJ/0n0jLsuxYzB9uo2EhBheeMFOqVIBZszI5vPP\nMxg0qA5XX70Au70OJpMFu70OVaosOefTgxBCFDd16/pZvz6TqVOzyc42MWSIMSPsDz8U71QiLSXi\nkhw/Di++aGPhQhsZGSbKlfMzYYKLPn08OBynn5fbhOl0xpKScjJ0BRZCiDBjscDAgR5uvdXL6NEO\nNm0yZoQdNcrNQw+5sRTDd2hpKRF/y/HjMGOGjYSEksydayc6OsC0adl8+WUGAwacGUiEEEJcWNWq\nAV5/PYsFC7KIiQkwbZqd9u2j2bOn+L1FBzWHKaWswDKgGuADBmit9wWzDOLSpKbCggU2Xn7ZxsmT\nJuLjT88zEh0d6tIJIUTRZjJB165e2rTx8vjjdlassNGhQzQDBngYM8ZFyZKhLmFwBDuG3QpYtNbN\ngKnAE0E+vvibUlNh5kyjZWT2bGMG1ilTjBlYBw6UQCKEEAWpTBmYO9fFm29mctVVAV56yUarVjF8\n/HHxuH3YFAgE7zYkpdQ1GEGkG3AHcJfWuucFdpP7pEIgNRWefRaSkuDECYiPh9GjYdAgZMIzIYQI\ngqwsmD4dZs4Erxd69oS5c6F8+VCX7LLlO5o32KHkSuAdoCQQD3TSWu+4wG6BSB8gGU6DQE+ehIUL\nbSxYYOPECRNly/oZNMhDYqL7spoPw6mOhUXqGBmkjpEhkuq4d28Uo0Y52L3bTOnSRmv13Xd7KVeu\naNbR6YzNN5QEu/vmEeADrXUtoB6wTCklQyPDQHo6zJ1ro1Gjkjz1lB2TCSZOdLFrVwZDh15eIBFC\nCHHprrvOz7p1mcyYkY3HA8OHl6Br1xIciMD1/YIdSo4DqTnfHwOsQPHoKAtT6enw3HM2GjWK4ckn\n7QQCMH68i9270yWMCCFEmDCboV8/D9u2ZXDzzV62b7dQt67xYdLtvvD+RUWwQ0kS0FAptRXYBIzX\nWmcEuQyCM8PI9Ol2fD4TY8caYWT4cAkjQggRjipXDrB8eRaLF2dRpgw8+aSddu2i2bUrMm4fDuot\nwVrrdKB7MI8pzpSRAUuXWpk3z8bRo1GUKhVg9GgXDzzgplSpUJdOCCHEhZhM0Lmzl65dYehQN6++\naqNjx2gSEz1MmFC0bx+OjGglLigzE+bPt3L99TFMnerA7TYxapTRMjJqlAQSIYQoakqXhtmzXbz7\nbiY1a/pZvNhGixYxbNhQdEdFSCiJcFlZsGCBEUamTHGQnW1ixAgjjIwe7SYuLtQlFEIIcTluuMHH\npk2ZjBrlIiXFRN++0fTr5+D334veOjoSSiJUVha8/LIRRiZPdpCVdTqMjB3rpnTpUJdQCCFEQbHb\nYfRoN5s2ZdK4sZf33rPSvHkMy5db8ftDXbqLJ6EkwmRnw8KFVho3jmHiRAcZGSaGD3exa5cRRsqU\nCXUJhRBCFBal/Lz7bhYzZ2YTCMCoUQ5uv70EBw4Ujbf7olFKcUHZ2bB4sRFGJkxwcPKkiaFDjXlG\nxo93U7ZsqEsohBAiGKKi4L77PGzfnkHHjh527rTQpk00s2bZcLlCXbq/JqGkiHO5YMkSK02axDBu\nnIO0NBNDhhhhZOJEN1dcIbP0CyFEcVShQoClS7N55ZUsrrgiwKxZdm68MZqdO8N3IKyEkiIiNXUt\nBw82Ze/eMhw82JSUlDd55RUrN9wQw9ixDk6cMDFokJsvv8xg8mQ38fESRoQQQsCtt3rZti2DxEQ3\nBw5E0aVLNI8+aictLdQlO5eEkiIgNXUtR44k4nLtxeOJYu3aZrRt25rRox0cO2bioYeMMDJligun\nU8KIEEKIM8XGwlNPuVi3LpPatX0sW2ajefMY1q2zEMQl8C5IQkkRkJIyG4/Hyrp1/enTZz9z5rzM\n8ePl6NFjOV98kcHjj7soVy6M/qqEEEKEpeuv9/PRR5mMHevi+HETiYkluPdeB7/8Eh63D0soCXMu\nF6xe3YrevQ8ye/ZCjh2rwJ13zmXFiqsZOLAf5ctLGBFCCHHxbDYYMcLNp59m0KyZlw0brLRoEcPi\nxVaOHz9zqEBq6tqglk1CSZjKyoJFi4y7aebOnUdqajzdus1hxYqrGTLkEa644jfs9tqhLqYQQogi\nqmbNAG+9lUVSUjZmM4wb56BrV8W+fQA+XK69HDmSGNRgIqEkzGRmnp6Bdfx4B6mpJvr3/44VK6oz\nePBI4uN/PfVcp3NECEsqhBCiqDOZoFcvY/XhG29cz969zRgw4GvWrBl+6jkpKXOCVh4JJWEiPR1e\neMFKo0bGDKwZGSaGDTNu7X3yyWr8859PYbfXASzY7XWoUmUJcXHdQl1sIYQQEaB8+QATJ3bmySc7\nEh//Cx9+2PvUz1yufUErR1BXCRbnOnkSFi2CZ56J4dixKGJjA4wY4eLBB8+cfTUurpuEECGEEIXG\nbq9N06bv07jx1fh81jO2B4uEkhBJTYWFC228/LKNEycgLs7E6NEuBgyQRfKEEEIEn9M5kiNHEjGb\n/ZjNrjzbgzdUIOihRCk1DugC2ID5WuvFwS5DKB0/Di+/bGPhQhtpaSbKlAnwxBPQs2c6sbGhLp0Q\nQojiKrc1PiVlDi7XPuz22jidI4LaSh/UUKKUag00A5oD0cCoYB4/lI4eNbFggZXFi22kp5uIj/cz\naZKb++93U716LCkpoS6hEEKI4i7UQwWC3VJyM/Ad8BZQCng0yMcPuj/+MPHiizaWLrWSmWnC6fTz\n6KMu+vb1EBMT6tIJIYQQ4cMUCOL8skqphcBVQCegOvAuUFtr/VeFKJKzg/36K8yaBQsWGHOOVKoE\nY8bAgAFQokSoSyeEEEKETL7Txwa7peQosE9r7Qa0UiobcAJ//NVOKSkng1G2AvHLLyZeeMHGq69a\ncblMVK7sZ+hQN3ff7cHhMG79TU8/cx+nM7ZI1fFSSB0jg9QxMkgdI0NRraPTmf8AymCHkm3AMKXU\nHKAiEIMRVIq8I0dMPPecjRUrrLjdJqpW9TNsmIsePTzYbKEunRBCCBH+ghpKtNbrlFItgS8wJm4b\nrLX2BbMMBe3HH40wsnKlFY/HRLVqfh55JJtu3bxYrRfeXwghhBCGoN8SrLUeHexjFoZDh0w8+6yd\n1ast+HwmatQwwkjXrl4sMvuLEEII8bfJ2+ffdPCgiaQkO2+8YcHvN1Grlo8RI9zcdpsXsznUpRNC\nCCGKLgklF2nfvijmzrXx1lsWAgET11zjY+RIN506eYmSFYSEEEKIyyah5AL27o0iKcnGe+8ZJdsZ\nzgAACCNJREFUYaROHSOM3HKLhBEhhBCiIEkoyce330Yxe7aN9euN0ar16/sYOdJF+/Y+TPneYS2E\nEEKISyWh5CxffRXFnDl2Nm40fjUJCT5GjXLRtq2EESGEEKIwSSjJ8eWXUcyebWfTJuNX0qSJl5Ej\n3bRqJWFECCGECIZiGUpSU9eSkjIbl2sf//nPPSQnz2DHjsoANG9uhJHmzSWMCCGEEMFU7EJJaupa\njhxJZM+eVixb9iF79rQBoFmz/zFmTBmaNi3Sc7kJIYQQRVaxCyUpKbP5/vvGPPLIpwA0bryePn2m\nkZBwkpo1d4S2cEIIIUQxVuxCicu1j6pVY7jvvsdo3Hg911zzZc72YverEEIIIcJKsXsntttrA3u5\n996p59kuhBBCiFApdtN/OZ0j89k+IsglEUIIIURexa6lJC6uGwApKXNwufZht9fG6RxxarsQQggh\nQqPYhRIwgomEECGEECK8mAKBQKjLIIQQQghR/MaUCCGEECI8SSgRQgghRFiQUCKEEEKIsCChRAgh\nhBBhQUKJEEIIIcKChBIhhBBChAUJJUIIIYQICyGbPE0pZQWWANUAOzAd+BlYBxzIedqLWutVefaJ\nAuYD9QAX0F9rfTCIxf5b8qnjPUCFnKdUA3ZqrXuetd9XQFrOw8Na6/uDUd5LoZQyAwsBBQSAgUA2\n8ErO438Dg7XW/jz7FKnzCPnW0wI8D/gw6tFXa/37WfsV9XNpJbKuyfPVcSIRdE0CKKXKAbuBdoCX\nCLse4Zw6OoigazGvs+pZggi6Hs8nlDO69gaOaq37KKXKAnuAqcAcrfXsfPa5HXBorZsqpW4AZgO3\nBae4l+ScOmqtqwIopcoAnwCP5N1BKeUATFrr1sEu7CXqDKC1bq6Uag08AZiAiVrrT5VSCzDO0Vt5\n9ilq5xHOX8/SwMNa6z1KqQeBMcCpRZQi5Fy+R2Rdk+fUUWt9G0TONZnzYeglICtn0xwi7Ho8Tx2f\nJbKuReC89Uwgsq7Hc4Sy+2YNMCnnexNGmk8AOiqltiilFiulYs/apwWwAUBrvRNoFKzCXqLz1THX\n48DzWutfz9qnHhCtlNqolNqU84cVtrTWbwMP5Dy8CjiBcR4352xbD9x01m5F7TzmV8+eWus9Odss\nGC1EeUXKuYyYazKfOuaKiGsSeAZYAPyS8zjirkfOrWNEXYt5nO9cRsz1eD4hCyVa63St9cmcX+pa\njCbUL4BHtdYtgUPAY2ftVgpIzfPYp5QK2/V78qljbnPcjRhNqmfLxPhDvBmjafm1cK4jgNbaq5Ra\nhtF8+hrGJ5Lc9QtOAnFn7VKkzmOus+uZ++allGoGDAGSztolEs5lRF2TcN46Rsw1qZS6D0jRWn+Q\nZ3NEXY/nq2MkXov5nMuIux7PFtKBrkqpKzGaS1/VWq8A3tJa78758VtAg7N2SQPyJsMorbWXMHae\nOgJ0A1ZorX3n2WU/kKy1Dmit9wNHgYrBKe2l01rfC9TC6K8vkedHsZz5aRSK4HnMlbeeSqkYpVQP\njE8yHbXWKWc9PRLO5cZIuybh3PNI5FyTiUA7pdSnQH1gOVAuz88j4Xo8p45KqQoReC2e71yuj8Tr\nMa+QhRKlVHlgIzBGa70kZ/MHSqnGOd/fiDG4J6/twK05+98AfBeMsl6qfOoIRvPp+nx2S8ToB0Qp\nVQkj+Z7dnBw2lFJ9lFLjch5mAn5gV05/PcAtwNazditS5xHyrWdXjE9lrbXWh86zWyScyzcj7Jo8\nXx39RMg1qbVuqbVulTN2Yg/QF1gfSddjPnW8iQi6FiHfer4TSdfj+YRslWCl1LNAD2Bfns0TgJmA\nB/gNeEBrnaaUWo7R9XEEY2TxPzHGaNyvtd5HmMqnjrcAu4DmWusTeZ6bW8ffMJqQq2KMlh+jtd4R\nrDL/XTmfMpdi3L1gBZ4C/oPxKduW8/0ArbWvqJ5HyLeeS4GfOP3Jc7PW+rEIO5c/Y3RzRMo1eU4d\ntdbvKKX2EiHXZK6cT9gDMUJXRF2PuXLqOBgjaEXMtXi2POcymgi6Hs8nZKFECCGEECIvmTxNCCGE\nEGFBQokQQgghwoKEEiGEEEKEBQklQgghhAgLEkqEEEIIERaK1ExvQoiiQSnVDRiH8T8mCliutZ6l\nlHoc+EhrffZcGSil9mit6yulpgBoracEschCiDAgLSVCiAKllKqMMVFVe611PaAp0FMp1QVoBZjP\nt5/Wun7wSimECEfSUiKEKGjxGBOTRWOskp2ulLoXYwbcRsAipdQdGJNAHQOuw5hk8GuttSn3RZRS\nZmAVcEhrPVop1QFjJXErcBhjErCjQayXEKKQSUuJEKJAaa2/Ad4BDimlvlBKPQ2YtdZTMWYz7q+1\nzp3++luttcqzwmsuE8YspD/nBBInxgyzN2utGwAfAE8HpUJCiKCRlhIhRIHTWj+klJoOtMdYmXWn\nUqrXeZ76eT4vMRBjNdvqOY+bYEwR/olSCowuoGMFWmghRMhJKBFCFCilVEegpNZ6FcY6M0uVUgOA\nfud5elY+L7MD+Ap4DrgLI4Rs01p3yTmGgzNXQxVCRADpvhFCFLRMYIZSqhqAUsoEXAt8DXi5uA9D\n32B0z9RRSnXCaFFpqpSqlfPzScCsAi63ECLEJJQIIQqU1voT4HFgnVJKY6ySbcYYpLoBWKCUanYR\nr+MGHgLmAekYy8+vVkp9BzQERhZODYQQoSKrBAshhBAiLEhLiRBCCCHCgoQSIYQQQoQFCSVCCCGE\nCAsSSoQQQggRFiSUCCGEECIsSCgRQgghRFiQUCKEEEKIsPD/tH5vdZOhxccAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b7e978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_option_stats(k_list, pv, de, ve)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Portfolio Valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, market players (asset managers, investment banks, hedge funds, insurance companies, etc.) have to value not only single derivatvies instruments but rather portfolios composed of several derivatives instruments. A consistent derivatives portfolio valuation is particularly important when there are multiple derivatives written on the same risk factor and/or correlations between different risk factors.\n",
    "\n",
    "These are the classes availble for a consistent portfolio valuation:\n",
    "\n",
    "* `derivatives_position` to model a portfolio position\n",
    "* `derivatives_portfolio` to model a derivatives portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### derivatives_position"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We work with the `market_environment` object from before and add information about the risk factor model we are using."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "me.add_constant('model', 'gbm')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A derivatives position consists of \"data only\" and not instantiated model or valuation objects. The necessary model and valuation objects are instantiated during the portfolio valuation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "put = derivatives_position(\n",
    "                name='put',  # name of position\n",
    "                quantity=1,  # number of instruments\n",
    "                underlyings=['gbm'],  # relevant risk factors\n",
    "                mar_env=me,  # market environment\n",
    "                otype='American single',  # the option type\n",
    "                payoff_func='np.maximum(40. - instrument_values, 0)')\n",
    "                    # the payoff funtion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method `get_info` prints an overview of the all relevant information stored for the respective `derivatives_position` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NAME\n",
      "put \n",
      "\n",
      "QUANTITY\n",
      "1 \n",
      "\n",
      "UNDERLYINGS\n",
      "['gbm'] \n",
      "\n",
      "MARKET ENVIRONMENT\n",
      "\n",
      "**Constants**\n",
      "initial_value 36.0\n",
      "volatility 0.2\n",
      "final_date 2015-12-31 00:00:00\n",
      "currency EUR\n",
      "frequency W\n",
      "paths 25000\n",
      "maturity 2015-12-31 00:00:00\n",
      "strike 40.0\n",
      "model gbm\n",
      "\n",
      "**Lists**\n",
      "\n",
      "**Curves**\n",
      "discount_curve <dx.frame.constant_short_rate object at 0x106799978>\n",
      "\n",
      "OPTION TYPE\n",
      "American single \n",
      "\n",
      "PAYOFF FUNCTION\n",
      "np.maximum(40. - instrument_values, 0)\n"
     ]
    }
   ],
   "source": [
    "put.get_info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### derivatives_portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `derivatives_portfolio` class implements the core portfolio valuation tasks. This sub-section illustrates to cases, one with uncorrelated underlyings and another one with correlated underlyings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Uncorrelated Underlyings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first example is based on a portfolio with two single-risk factor instruments on **two different risk factors which are not correlated**. In addition to the `gbm` object, we define a `jump_diffusion` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "me_jump = market_environment('me_jump', dt.datetime(2015, 1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "me_jump.add_environment(me)\n",
    "me_jump.add_constant('lambda', 0.8)\n",
    "me_jump.add_constant('mu', -0.8)\n",
    "me_jump.add_constant('delta', 0.1)\n",
    "me_jump.add_constant('model', 'jd')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on this new risk factor model object, a European call option is defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "call_jump = derivatives_position(\n",
    "                name='call_jump',\n",
    "                quantity=3,\n",
    "                underlyings=['jd'],\n",
    "                mar_env=me_jump,\n",
    "                otype='European single',\n",
    "                payoff_func='np.maximum(maturity_value - 36., 0)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our **relevant market** now takes on the following form (defined a `dictionary` objects):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "risk_factors = {'gbm': me, 'jd' : me_jump}\n",
    "positions = {'put' : put, 'call_jump' : call_jump}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To instantiate the `derivatives_portfolio` class, a **valuation environment** (instance of `market_environment` class) is needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "val_env = market_environment('general', dt.datetime(2015, 1, 1))\n",
    "val_env.add_constant('frequency', 'M')\n",
    "val_env.add_constant('paths', 50000)\n",
    "val_env.add_constant('starting_date', val_env.pricing_date)\n",
    "val_env.add_constant('final_date', val_env.pricing_date)\n",
    "val_env.add_curve('discount_curve', r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the **instantiation**, we pass all the elements to the portfolio class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "port = derivatives_portfolio(\n",
    "            name='portfolio',  # name \n",
    "            positions=positions,  # derivatives positions\n",
    "            val_env=val_env,  # valuation environment\n",
    "            risk_factors=risk_factors, # relevant risk factors\n",
    "            correlations=False,  # correlation between risk factors\n",
    "            fixed_seed=False,  # fixed seed for randon number generation\n",
    "            parallel=False)  # parallel valuation of portfolio positions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once instantiated, the method `get_statistics` provides major portfolio statistics like position values, position deltas ans position vegas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Totals\n",
      " pos_value    34.7260\n",
      "pos_delta     2.2706\n",
      "pos_vega     22.1461\n",
      "dtype: float64\n",
      "CPU times: user 838 ms, sys: 64.4 ms, total: 902 ms\n",
      "Wall time: 885 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "stats = port.get_statistics()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>position</th>\n",
       "      <th>name</th>\n",
       "      <th>quantity</th>\n",
       "      <th>otype</th>\n",
       "      <th>risk_facts</th>\n",
       "      <th>value</th>\n",
       "      <th>currency</th>\n",
       "      <th>pos_value</th>\n",
       "      <th>pos_delta</th>\n",
       "      <th>pos_vega</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>put</td>\n",
       "      <td>put</td>\n",
       "      <td>1</td>\n",
       "      <td>American single</td>\n",
       "      <td>[gbm]</td>\n",
       "      <td>4.432</td>\n",
       "      <td>EUR</td>\n",
       "      <td>4.432</td>\n",
       "      <td>-0.6571</td>\n",
       "      <td>10.9231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>call_jump</td>\n",
       "      <td>call_jump</td>\n",
       "      <td>3</td>\n",
       "      <td>European single</td>\n",
       "      <td>[jd]</td>\n",
       "      <td>10.098</td>\n",
       "      <td>EUR</td>\n",
       "      <td>30.294</td>\n",
       "      <td>2.9277</td>\n",
       "      <td>11.2230</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    position       name  quantity            otype risk_facts   value  \\\n",
       "0        put        put         1  American single      [gbm]   4.432   \n",
       "1  call_jump  call_jump         3  European single       [jd]  10.098   \n",
       "\n",
       "  currency  pos_value  pos_delta  pos_vega  \n",
       "0      EUR      4.432    -0.6571   10.9231  \n",
       "1      EUR     30.294     2.9277   11.2230  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method returns a standard pandas `DataFrame` object with which you can work as you are used to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pos_value    34.7260\n",
       "pos_delta     2.2706\n",
       "pos_vega     22.1461\n",
       "dtype: float64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats[['pos_value', 'pos_delta', 'pos_vega']].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The metod `get_values` only calculates the present values of the derivatives instruments and positions and is therefore a bit less compute and time intensive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total\n",
      " pos_value    34.438908\n",
      "dtype: float64\n",
      "CPU times: user 191 ms, sys: 14.3 ms, total: 206 ms\n",
      "Wall time: 199 ms\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>position</th>\n",
       "      <th>name</th>\n",
       "      <th>quantity</th>\n",
       "      <th>otype</th>\n",
       "      <th>risk_facts</th>\n",
       "      <th>value</th>\n",
       "      <th>currency</th>\n",
       "      <th>pos_value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>put</td>\n",
       "      <td>put</td>\n",
       "      <td>1</td>\n",
       "      <td>American single</td>\n",
       "      <td>[gbm]</td>\n",
       "      <td>4.449000</td>\n",
       "      <td>EUR</td>\n",
       "      <td>4.449000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>call_jump</td>\n",
       "      <td>call_jump</td>\n",
       "      <td>3</td>\n",
       "      <td>European single</td>\n",
       "      <td>[jd]</td>\n",
       "      <td>9.996636</td>\n",
       "      <td>EUR</td>\n",
       "      <td>29.989908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    position       name  quantity            otype risk_facts     value  \\\n",
       "0        put        put         1  American single      [gbm]  4.449000   \n",
       "1  call_jump  call_jump         3  European single       [jd]  9.996636   \n",
       "\n",
       "  currency  pos_value  \n",
       "0      EUR   4.449000  \n",
       "1      EUR  29.989908  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time port.get_values()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method `get_positions` provides detailed information about the single derivatives positions of the `derivatives_portfolio` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "--------------------------------------------------\n",
      "NAME\n",
      "put \n",
      "\n",
      "QUANTITY\n",
      "1 \n",
      "\n",
      "UNDERLYINGS\n",
      "['gbm'] \n",
      "\n",
      "MARKET ENVIRONMENT\n",
      "\n",
      "**Constants**\n",
      "initial_value 36.0\n",
      "volatility 0.2\n",
      "final_date 2015-12-31 00:00:00\n",
      "currency EUR\n",
      "frequency M\n",
      "paths 50000\n",
      "maturity 2015-12-31 00:00:00\n",
      "strike 40.0\n",
      "model gbm\n",
      "starting_date 2015-01-01 00:00:00\n",
      "\n",
      "**Lists**\n",
      "time_grid [datetime.datetime(2015, 1, 1, 0, 0) datetime.datetime(2015, 1, 31, 0, 0)\n",
      " datetime.datetime(2015, 2, 28, 0, 0) datetime.datetime(2015, 3, 31, 0, 0)\n",
      " datetime.datetime(2015, 4, 30, 0, 0) datetime.datetime(2015, 5, 31, 0, 0)\n",
      " datetime.datetime(2015, 6, 30, 0, 0) datetime.datetime(2015, 7, 31, 0, 0)\n",
      " datetime.datetime(2015, 8, 31, 0, 0) datetime.datetime(2015, 9, 30, 0, 0)\n",
      " datetime.datetime(2015, 10, 31, 0, 0)\n",
      " datetime.datetime(2015, 11, 30, 0, 0)\n",
      " datetime.datetime(2015, 12, 31, 0, 0)]\n",
      "correlation_matrix      gbm   jd\n",
      "gbm  1.0  0.0\n",
      "jd   0.0  1.0\n",
      "cholesky_matrix [[1. 0.]\n",
      " [0. 1.]]\n",
      "random_numbers [[[ 1.59911088 -1.4046112  -1.41690211 ... -0.02367133  0.64452581\n",
      "    0.83372797]\n",
      "  [-1.71068746 -0.17718321  1.19908444 ... -0.12887556  1.84851716\n",
      "    1.99223491]\n",
      "  [ 0.91793265  0.527942   -0.51603028 ...  0.84100797 -1.36662164\n",
      "   -0.60581475]\n",
      "  ...\n",
      "  [ 1.2128477  -0.02445883  0.28700922 ... -0.68947286 -0.04293013\n",
      "   -0.15945594]\n",
      "  [-1.32537389 -0.70003276  1.90365643 ... -0.2332303  -0.0369755\n",
      "    1.44280306]\n",
      "  [ 0.20542848 -0.7790572  -0.75625624 ... -1.470969   -1.00645074\n",
      "   -0.12511486]]\n",
      "\n",
      " [[-2.1046119   1.11433037 -1.44243622 ...  0.95216647 -0.4916233\n",
      "    0.14714287]\n",
      "  [ 0.88624348 -0.10835483  1.09678341 ... -0.02139183  1.17828289\n",
      "   -0.6156402 ]\n",
      "  [-0.49969036 -1.61494765 -0.6953123  ...  0.09100147  1.12869001\n",
      "   -0.65676166]\n",
      "  ...\n",
      "  [ 0.04256569  0.51287869  0.39970509 ...  2.38658577  1.64993773\n",
      "   -0.16761589]\n",
      "  [ 0.69762962  0.89591537  0.14343585 ... -0.62170926  0.95533176\n",
      "   -0.03614675]\n",
      "  [-0.88760744 -1.24120179  2.66507407 ...  0.40644798 -1.64541865\n",
      "    1.36340621]]]\n",
      "rn_set {'jd': 1, 'gbm': 0}\n",
      "\n",
      "**Curves**\n",
      "discount_curve <dx.frame.constant_short_rate object at 0x106799978>\n",
      "\n",
      "OPTION TYPE\n",
      "American single \n",
      "\n",
      "PAYOFF FUNCTION\n",
      "np.maximum(40. - instrument_values, 0)\n",
      "\n",
      "--------------------------------------------------\n",
      "\n",
      "--------------------------------------------------\n",
      "NAME\n",
      "call_jump \n",
      "\n",
      "QUANTITY\n",
      "3 \n",
      "\n",
      "UNDERLYINGS\n",
      "['jd'] \n",
      "\n",
      "MARKET ENVIRONMENT\n",
      "\n",
      "**Constants**\n",
      "initial_value 36.0\n",
      "volatility 0.2\n",
      "final_date 2015-12-31 00:00:00\n",
      "currency EUR\n",
      "frequency M\n",
      "paths 50000\n",
      "maturity 2015-12-31 00:00:00\n",
      "strike 40.0\n",
      "model jd\n",
      "lambda 0.8\n",
      "mu -0.8\n",
      "delta 0.1\n",
      "starting_date 2015-01-01 00:00:00\n",
      "\n",
      "**Lists**\n",
      "time_grid [datetime.datetime(2015, 1, 1, 0, 0) datetime.datetime(2015, 1, 31, 0, 0)\n",
      " datetime.datetime(2015, 2, 28, 0, 0) datetime.datetime(2015, 3, 31, 0, 0)\n",
      " datetime.datetime(2015, 4, 30, 0, 0) datetime.datetime(2015, 5, 31, 0, 0)\n",
      " datetime.datetime(2015, 6, 30, 0, 0) datetime.datetime(2015, 7, 31, 0, 0)\n",
      " datetime.datetime(2015, 8, 31, 0, 0) datetime.datetime(2015, 9, 30, 0, 0)\n",
      " datetime.datetime(2015, 10, 31, 0, 0)\n",
      " datetime.datetime(2015, 11, 30, 0, 0)\n",
      " datetime.datetime(2015, 12, 31, 0, 0)]\n",
      "correlation_matrix      gbm   jd\n",
      "gbm  1.0  0.0\n",
      "jd   0.0  1.0\n",
      "cholesky_matrix [[1. 0.]\n",
      " [0. 1.]]\n",
      "random_numbers [[[ 1.59911088 -1.4046112  -1.41690211 ... -0.02367133  0.64452581\n",
      "    0.83372797]\n",
      "  [-1.71068746 -0.17718321  1.19908444 ... -0.12887556  1.84851716\n",
      "    1.99223491]\n",
      "  [ 0.91793265  0.527942   -0.51603028 ...  0.84100797 -1.36662164\n",
      "   -0.60581475]\n",
      "  ...\n",
      "  [ 1.2128477  -0.02445883  0.28700922 ... -0.68947286 -0.04293013\n",
      "   -0.15945594]\n",
      "  [-1.32537389 -0.70003276  1.90365643 ... -0.2332303  -0.0369755\n",
      "    1.44280306]\n",
      "  [ 0.20542848 -0.7790572  -0.75625624 ... -1.470969   -1.00645074\n",
      "   -0.12511486]]\n",
      "\n",
      " [[-2.1046119   1.11433037 -1.44243622 ...  0.95216647 -0.4916233\n",
      "    0.14714287]\n",
      "  [ 0.88624348 -0.10835483  1.09678341 ... -0.02139183  1.17828289\n",
      "   -0.6156402 ]\n",
      "  [-0.49969036 -1.61494765 -0.6953123  ...  0.09100147  1.12869001\n",
      "   -0.65676166]\n",
      "  ...\n",
      "  [ 0.04256569  0.51287869  0.39970509 ...  2.38658577  1.64993773\n",
      "   -0.16761589]\n",
      "  [ 0.69762962  0.89591537  0.14343585 ... -0.62170926  0.95533176\n",
      "   -0.03614675]\n",
      "  [-0.88760744 -1.24120179  2.66507407 ...  0.40644798 -1.64541865\n",
      "    1.36340621]]]\n",
      "rn_set {'jd': 1, 'gbm': 0}\n",
      "\n",
      "**Curves**\n",
      "discount_curve <dx.frame.constant_short_rate object at 0x106799978>\n",
      "\n",
      "OPTION TYPE\n",
      "European single \n",
      "\n",
      "PAYOFF FUNCTION\n",
      "np.maximum(maturity_value - 36., 0)\n",
      "\n",
      "--------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "port.get_positions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Correlated Underlyings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second example case is exactly the same but now with a **highly positive correlation** between the two relevant risk factors. Correlations are to be provided as a `list`  of `list` objects using the risk factor model names to reference them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "correlations = [['gbm', 'jd', 0.9]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Except from now passing this new object, the application and usage remains the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "port = derivatives_portfolio(\n",
    "            name='portfolio',\n",
    "            positions=positions,\n",
    "            val_env=val_env,\n",
    "            risk_factors=risk_factors,\n",
    "            correlations=correlations,\n",
    "            fixed_seed=True,\n",
    "            parallel=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Totals\n",
      " pos_value    35.1350\n",
      "pos_delta     1.6345\n",
      "pos_vega     21.8606\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>position</th>\n",
       "      <th>name</th>\n",
       "      <th>quantity</th>\n",
       "      <th>otype</th>\n",
       "      <th>risk_facts</th>\n",
       "      <th>value</th>\n",
       "      <th>currency</th>\n",
       "      <th>pos_value</th>\n",
       "      <th>pos_delta</th>\n",
       "      <th>pos_vega</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>put</td>\n",
       "      <td>put</td>\n",
       "      <td>1</td>\n",
       "      <td>American single</td>\n",
       "      <td>[gbm]</td>\n",
       "      <td>4.433</td>\n",
       "      <td>EUR</td>\n",
       "      <td>4.433</td>\n",
       "      <td>-0.6548</td>\n",
       "      <td>10.8335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>call_jump</td>\n",
       "      <td>call_jump</td>\n",
       "      <td>3</td>\n",
       "      <td>European single</td>\n",
       "      <td>[jd]</td>\n",
       "      <td>10.234</td>\n",
       "      <td>EUR</td>\n",
       "      <td>30.702</td>\n",
       "      <td>2.2893</td>\n",
       "      <td>11.0271</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    position       name  quantity            otype risk_facts   value  \\\n",
       "0        put        put         1  American single      [gbm]   4.433   \n",
       "1  call_jump  call_jump         3  European single       [jd]  10.234   \n",
       "\n",
       "  currency  pos_value  pos_delta  pos_vega  \n",
       "0      EUR      4.433    -0.6548   10.8335  \n",
       "1      EUR     30.702     2.2893   11.0271  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port.get_statistics()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **Cholesky matrix** has been added to the valuation environment (which gets passed to the risk factor model objects)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.        ],\n",
       "       [0.9       , 0.43588989]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port.val_env.lists['cholesky_matrix']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us pick **two specific simulated paths**, one for each risk factor, and let us visualize these."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "path_no = 0\n",
    "paths1 = port.underlying_objects['gbm'].get_instrument_values()[:, path_no]\n",
    "paths2 = port.underlying_objects['jd'].get_instrument_values()[:, path_no]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot illustrates that the two paths are indeed **highly positively correlated**. However, in this case a **large jump** occurs for the `jump_diffusion` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PVOp1NY61v+Fv3Ybsl6ZgVasW8ecpiWPVtmE9yX1uxrXoG0J16pLzwkQCzVtE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fdeacf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(port.time_grid, paths1, 'r', label='gbm')\n",
    "plt.plot(port.time_grid, paths2, 'b', label='jd')\n",
    "plt.gcf().autofmt_xdate()\n",
    "plt.legend(loc=0); plt.grid(True)\n",
    "# highly correlated underlyings\n",
    "# -- with a large jump for one risk factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Copyright, License & Disclaimer**\n",
    "\n",
    "© Dr. Yves J. Hilpisch | The Python Quants GmbH\n",
    "\n",
    "DX Analytics (the \"dx library\" or \"dx package\") is licensed under the GNU Affero General\n",
    "Public License version 3 or later (see http://www.gnu.org/licenses/).\n",
    "\n",
    "DX Analytics comes with no representations or warranties, to the extent\n",
    "permitted by applicable law.\n",
    "\n",
    "http://tpq.io | [dx@tpq.io](mailto:team@tpq.io) |\n",
    "http://twitter.com/dyjh\n",
    "\n",
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "**Quant Platform** | http://pqp.io\n",
    "\n",
    "**Python for Finance Training** | http://training.tpq.io\n",
    "\n",
    "**Certificate in Computational Finance** | http://compfinance.tpq.io\n",
    "\n",
    "**Derivatives Analytics with Python (Wiley Finance)** |\n",
    "http://dawp.tpq.io\n",
    "\n",
    "**Python for Finance (2nd ed., O'Reilly)** |\n",
    "http://py4fi.tpq.io"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
